Offset-fed multi-beam tracking antenna system utilizing especially shaped reflector surfaces

Abstract

A reflector antenna system is described suitable for ground stations used in communication with geostationary satellites. Dual beams or multi-beams can be directed at several satellites spaced angularly from 5° to 20° apart and these beams are scanned by feed motion keeping a single main reflector surface fixed. Offset feed geometry is used for low aperture blocking and shaping of subreflectors and main reflector results in very high aperture efficiencies, low sidelobes and symmetric low cross-polarization patterns needed for satellite links. A novel method for shaping subreflectors using the ratios of ray lengths squared and variable focal lengths is applied in the optimally tilted offset geometry results in almost uniform aperture power distributions. A new general procedure for shaping doubly curved surfaces intercepting a known population of rays such that these rays are focused to a point or reflected in a given direction is used to shape the main reflector for elimination of aperture phase errors and to shape a second subreflector which focuses perfectly to the apex of a second feed horn.

What is claimed is: 
     
       1. An antenna system for radiating and receiving electromagnetic energy at frequencies above 30 mHz comprising: two shaped subreflectors being generally separated, non-conic section surfaces and each separately being illuminated and fed by one or more horn radiators and one of the said shaped subreflectors with its illuminating horn radiator or horn radiators being called herein the principal feed and other shaped subreflector with illuminating horn radiator or horn radiators being called herein the secondary feed; and   a shaped main reflector being also generally a non-conic section surface mounted in a position fixed with respect to a fixed frame of coordinates referred to the earth's surface and said shaped main reflector being illuminated independently by said principal feed and said secondary feed such that said antenna system produces one or more antenna radiation pattern or patterns each with a main antenna beam pointed in a direction corresponding to the locations and orientations of the main shaped reflector, one of the shaped subreflectors, and one of the horn radiators; and   the orientation of said shaped main reflectors with respect to that of the principal feed and the secondary feed being an offset position such that electromagnetic energy radiated to and from the said principal feed and said secondary feed to illuminate said shaped main reflector is largely unobstructed and the electromagnetic energy passing to and from the shaped main reflector surface from signal sources located in directions of said antenna main beams is also largely unobstructed, said orientation of the main shaped subreflector with respect to the principal feed and the secondary feed being referred to a plane of left-right symmetry which divides the shaped main reflector surface and the two shaped subreflector surfaces into nearly equal left-right symmetric portions and such that the center of the shaped subreflector surfaces, the directions of the axes of the several horn radiators and the direction of the antenna main beams all lie approximately in said plane of left-right symmetry, and the orientation of the two shaped subreflectors is such as to position one shaped subreflector above the other and such that the focal region of the main reflector lies between the said two shaped subreflectors and the shaped main reflector; and   the shapes of said shaped subreflectors and said shaped main reflector being constructed to produce a prescribed electromagnetic power and phase distribution over the aperture of the shaped main reflector which distribution includes a nearly uniform power and phase aperture distribution when said shaped subreflectors and main reflector are illuminated by said horn radiators and antenna portions are oriented and positioned as specified above to produce said antenna patterns and antenna beams; and   said antenna beams being scanned in angular directions by changing the positions of said two subreflectors and their horn radiators with respect to the fixed shaped main reflector position by means of moveable supports and apparatus attached to said two shaped subreflectors and to said horn radiators such that the changed positions of the shaped subreflectors and the horn radiators enable the antenna beams to track angular changes in signal source directions.   
     
     
       2. The antenna system of claim 1 wherein one of said conical horn radiators is attached to one of said shaped subreflectors along portions of the edge of the subreflector and wherein an oval shaped orifice is cut out of the wall of the conical horn radiator to allow unobstructed radiation and reception of electromagnetic energy to proceed through a focal region between said main reflector and said shaped subreflector such said oval orifice being for the purpose of radiating energy to and from the said horn radiator and said subreflector with reduced spillover losses. 
     
     
       3. The antenna system of claim 1 wherein the secondary feed receives and transmits electromagnetic power with radiation patterns having main beams in directions at least one degree in angle remote from directions of the main beams of radiation patterns produced by said principal feed; and said electromagnetic power when received by said shaped main reflector surface is reflected therefrom and impinges on a second shaped subreflector of the secondary feed, herein called the second shaped subreflector, and is reflected therefrom to a point or a small region at which point or small region is located the phase center of a horn radiator, herein called the second horn radiator; and   the shape of the surface of the second shaped subreflector and the positions of the second horn radiator and the second shaped subreflector are constructed such that the transmitted radition patterns produced by the secondary feed when electromagnetic power is radiated by said second horn radiator onto the second shaped subreflector which in turn illuminates said shaped main reflector has approximately the same beamwidth for all cross sections measured through its main beam and levels of secondary radiation lobes not appreciably higher than the antenna radiation patterns produced by said principal feed.   
     
     
       4. An antenna system for radiating and receiving electromagnetic energy at frequencies above 30 mHz comprising: two shaped subreflectors being generally separated, non-conic section surfaces and each separately being illuminated and fed by one or more horn radiators and one of the said shaped subreflectors with its illuminating horn radiator or horn radiators being called herein the principal feed and other shaped subreflector with illuminating horn radiator or horn radiators being called herein the secondary feed; and   the principal subreflector is so shaped that electromagnetic power radiated from the said horn radiator is radiated along rays from the phase center of said horn radiator a distance r 1  to the interior reflecting surface of said shaped subreflector whereupon it is reflected toward a focal point having a position determined such that the ray path r 2  from the said reflector surface to the focal point F Q  and the ray path continuing on from said focal point F Q  to a reference paraboloid surface proximate to the said main reflector a distance ρ such that the squared values of the ray lengths r 1  r 2  and ρ obey the equation (1) ##EQU28##  where in equation (1), k o  is a constant and G(θ o , φ o ) represents the power pattern of said horn radiator as a function of θ o  an angle measured from the axis of said horn radiator and of φ o  a spherical angle coordinate orthogonal to θ o  and whereby the shape of said shaped subreflector satisfies equation (1) for successive points projected along the said subreflector surface according to equation (2) which expresses Snell's Law of reflection:   r.sub.2 =r.sub.1 -2(r.sub.1 ·n)n                  (2)        wherein r 1 , r 2 , and n are unit vectors lying in the direction of rays r 1  and r 2  and n is directed normal to said subreflector and from the unit vector n, we write   n=a.sub.m n+b.sub.n y+c.sub.n z        wherein a n , b n , and c n  are components of vector n in directions of unit vectors x, y, z which are directed along the axis of the rectangular coordinates used to describe the said shaped subreflector and from the values a n , b n , c n , and by use of equation (3) for the partial derivative ∂z/∂x and ∂z/∂y ##EQU29##  and whereby successive points on said shaped subreflector are located according to the numerical projector equations (4),(5),(6): ##EQU30##   x.sub.i+1 =x.sub.i +Δx                               (5)       y.sub.i+1 =y.sub.i                                         ( 6)        for x cuts across said shaped surface and ##EQU31##   y.sub.i+1 =y.sub.i +Δy                               (8)       x.sub.i+1 =x.sub.i                                         ( 9)        for y cuts across said shaped surface and the terms ##EQU32##  are values of the partial derivatives from earlier points obtained for determining the shape of said subreflector surface; and   a shaped main reflector being also generally non-conic section surface mounted in a position fixed with respect to a frame of coordinates referred to the earth's surface and said shaped main reflector being illuminated independently by said principal feed and said secondary feed such that said antenna system produces one or more antenna radiation pattern or patterns each with a main antenna beam pointed in a direction corresponding to the locations and orientations of the main shaped reflector, one of the shaped subreflectors, and one of the horn radiators; and   the orientation of said shaped main reflector with respect to that of the principal feed and the secondary feed being an offset position such that electromagnetic energy radiated to and from the said principal feed and said secondary feed to illuminate said shaped main reflector is largely unobstructed and the electromagnetic energy passing to and from the shaped main reflector surface from signal sources located in directions of said antenna main beams is also largely unobstructed, said orientation of the main shaped subreflector with respect to the principal feed and the secondary feed being referred to a plane of left-right symmetry which divides the shaped main reflector surface and the two shaped subreflector surfaces into nearly equal left-right symmetric portions and such that the center of the shaped main reflector surface and the centers of the shaped subreflector surfaces, the direction of the antenna main beams all lie approximately in said plane of left-right symmetry, and the orientation of the two shaped subreflectors is such as to position one shaped subreflector above the other and such that the focal region of the main reflector lies between the said two shaped subreflectors and the shaped main reflector; and   the shapes of said shaped subreflectors and said shaped main reflector being constructed to produce a prescribed electromagnetic power and phase distribution over the aperture of the shaped main reflector which distribution includes a nearly uniform power and phase aperture distribution when said shaped subreflectors and main reflector are illuminated by said horn radiators and antenna portions are oriented and positioned as specified above to produce said antenna patterns and antenna beams and   said antenna beams being scanned in angular directions by changing the positions of said two subreflectors and their horn radiators with respect to the fixed shaped main reflector position by means of moveable supports and apparatus attached to said two shaped subreflectors and to said horn radiators such that the changed positions of the shaped subreflectors and the horn radiators enable the antenna beams to track angular changes in signal source directions.   
     
     
       5. A shaped subreflector surface illuminated by electromagnetic power from a radiator which power, upon reflection from said shaped subreflector surfaces, illuminates a main reflector and said shaped subreflector surface is so shaped that the electromagnetic power radiated from said radiator is radiated along rays from the phase center of said radiator a distance r 1  to the interior reflecting surface of said shaped subreflector whereupon it is reflected toward a focal point having a position determined such that the ray path r 2  from the said reflector surface to the focal point F Q  and the ray path continuing on from said focal point F Q  to a reference paraboloid surface proximate to the said main reflector a distance ρ such that the squared values of the ray lengths r 1 , r 2 , and ρ obey the equation (1) ##EQU33## where in equation (1), k o  is a constant and G(θ o , φ o ) represents the power pattern of said radiator as a function of θ o  an angle measured from the axis of said radiator and of φ o  a spherical angle coordinate orthogonal to θ o  and whereby the shape of said shaped subreflector satisfies equation (1) for successive points projected along the said subreflector surface by calculating normal vectors to the said subreflector surface according to equation (2) which expresses Snell's Law of reflection:   r.sub.2 =r.sub.1 -z(r.sub.1 ·n)n                  (2)     wherein r 1 , r 2 , and n are unit vectors lying in the direction of rays r 1  and r 2  and n is directed normal to said subreflector and from the unit vector n, we write     n=a.sub.n x+b.sub.n y+c.sub.n z     wherein a n , b n , and c n  are components of vector n in directions of unit vectors x, y, z which are directed along the axis of the rectangular coordinates used to describe the said shaped subreflector and from the values a n , b n , c n , and by use of equation (3) for the partial derivative ∂z/∂x and ∂z/∂y ##EQU34## and whereby successive points on said shaped subreflector are located according to the numerical projector equations (4),(5),(6): ##EQU35##     x.sub.i+1 =x.sub.i +Δx                               (5)       y.sub.i+1 =y.sub.i                                         ( 6)     for x cuts across said shaped surface and ##EQU36##     y.sub.i+1 =y.sub.i +Δy                               (8)       x.sub.i+1 =x.sub.i                                         ( 9)     for y cuts across said shaped surface and the terms ##EQU37## are values of the partial derivatives from earlier points obtained for determining the shape of said subreflector surface.   
     
     
       6. A reflector antenna functioning in transmitting and receiving modes comprising: a shaped reflector and an illuminating feed wherein,   the shape of the reflecting surface of the shaped reflector is determined by the radiation pattern of the illuminating feed such that said reflector antenna produces an antenna pattern having a main beam with antenna gain of the approximate form csc 2  θ in a given plane where θ is the spherical coordinate angle in said given plane θ being approximately zero at the peak of said main beam and where φ is the spherical coordinate angle in planes orthogonal to θ in which plane said main beam has a narrow nearly constant angular beamwidth such that the said main beam is fan-shaped in form and when θ is the elevation angle plane measured from the horizon toward the zenith of a radar mounted on the surface of the earth then the radar signals transmitted and subsequently received by said reflector antenna functioning with said radar from a reflecting target flying at a constant altitude above the surface of the earth are nearly constant; and   said shaped reflector being a doubly curved surface constructed by connecting points on the reflector surface determined at successive points by finding through interpolation at or near the interception points on the reflecting surface of said rays obtained from the radiation pattern of said illuminating feed and by extrapolation along the reflection surface to successive points by finding normals to and partial derivatives of the reflecting surface under construction through use of said rays and points on the reflecting surface previously determined so that the main beam of the radiation pattern produced by said reflector antenna has the approximate gain function in either the receiving or transmitting mode of csc 2  θ in the θ plane and narrow angular beamwidths in said θ plane orthogonal to the θ plane and at certain values of the angle θ the main beam is focused to points at specified distances from the antenna to further reduce the angular beamwidths in θ planes of the antenna patterns.   
     
     
       7. The reflector antenna of claim 6 wherein said illuminating feed comprises a horn radiator. 
     
     
       8. The reflector antenna of claim 6 wherein said illuminating feed comprises a horn radiator and a shaped subreflector in offset position with respect to the reflector antenna surface such that electromagnetic radiation passing to and from portions of the reflector antenna is unobstructed. 
     
     
       9. An antenna system for radiating and receiving electromagnetic energy comprising: one or more shaped subreflector or subreflectors, generally not conic sections in form, each illuminated by one or more radiator or radiators; and each radiator together with the subreflector that it illuminates constituting separate antenna feeds, which feeds illuminate a common shaped main reflector whose central portion is tangent to a reference offset paraboloidal section and said main reflector edge contour dimensions are dependent on the radiation pattern of one of the radiators;   and said shaped subreflector or subreflectors and their radiator or radiators are positioned and moved with their central portions lying approximately in a plane containing the central point on the shaped main reflector surface and the axis of said reference offset paraboloidal section such that the electromagnetic energy passing to and from the shaped main reflector and to and from any radiator or shaped subreflector is largely unobstructed;   and the antenna system produces one or more radiation patterns each with a nearly circularly symmetric main beam that can be steered in direction by motions of a radiator and a subreflector;   and the antenna gain and pattern sidelobes of one of the radiation patterns are controlled by shaping the reflecting surface of one of the shaped subreflectors and by shaping the reflecting surface of the shaped main reflector.   
     
     
       10. The antenna systems of claims 1 and 9 wherein the shaped main reflector and one of the shaped subreflectors are approximately conic sections in form, said shaped main reflector having a reflecting surface paraboloidal in form, and said shaped subreflector being a surface of revolution with elliptical or hyperbolic cross section is illuminated by two or more radiators to produce two or more independent antenna patterns with main beams in two or more given directions and with secondary pattern maxima below 15 dB; and wherein the forms of the caustic focal fields in one of the focal regions of the shaped subreflector when illuminated by each of the several horns are of similar form and position to the caustic fields in the region of the caustic fields of said shaped main reflector when the shaped main reflector receives plane waves from said given directions.   
     
     
       11. The antenna system of claim 9 wherein the metal reflecting surface of one of the shaped subreflectors is so shaped that electromagnetic power radiated from the said radiator is radiated along rays from the phase center of said radiator a distance r 1  to the interior reflecting surface of said shaped subreflector whereupon it is reflected toward a focal point having a position determined such that the ray path r 2  from the said reflector surface of the focal point F Q  and the ray path continuing on from said focal point F Q  to a reference paraboloid surface proximate to the said main reflector a distance ρ such that the squared values of the ray lengths r 1 , r 2  and ρ obey the equation (1) ##EQU38## where in equation (1), k o  is a constant and G(θ o , φ o ) represents the power pattern of said radiator as a function of θ o  an angle measured from the axis of said radiator and of φ o  a spherical angle coordinate orthogonal to θ o  and whereby the shape of said shaped subreflector satisfied equation (1) for successive points projected along the said subreflector surface by calculating normal vectors to the said subreflector surface according to equation (2) which expresses Snell's Law of reflection:   r.sub.2 =r.sub.1 -2(r.sub.1 ·n)n                  (2)     wherein r 1 , r 2 , and n are unit vectors lying in the direction of rays r 1  and r 2  and n is directed normal to said subreflector and from the unit vector n, we write     n=a.sub.n x+b.sub.n y+c.sub.n z     wherein a n , b n , and c n  are components of vector n in directions of unit vectors x, y, z which are directed along the axis of the rectangular coordinates used to describe the said shaped subreflector and from the values a n , b n , c n , and by use of equation (3) for the partial derivative ∂z/∂x and ∂z/∂y ##EQU39##  and whereby successive points on said shaped subreflector are located according to the numerical projector equations (4), (5), (6): ##EQU40##     x.sub.i+1 =X.sub.i +ΔX                               (5)       Y.sub.i+1 =Y.sub.i                                         ( 6)     for x cuts across said shaped surface and ##EQU41##     Y.sub.i+1 =Y.sub.i +ΔY                               (8)       X.sub.i+1 =X.sub.i                                         ( 9)     for y cuts across said shaped surface and the terms ##EQU42## are values of the partial derivatives from earlier points obtained for determining the shape of said subreflector surface.   
     
     
       12. The antenna systems of claims 1 and 9 wherein said radiator or radiators and said subreflector or subreflectors are each independently positioned and moved with respect to the location and orientation of said main reflector in a manner that independently directs each main beam of said antenna patterns in a given direction, the motion and positioning of each radiator and subreflector being so controlled that the form of the caustic focal fields produced by the subreflector when illuminated the radiator has the same general structure and lies in approximately the same position as the caustic focal fields produced when the main reflector receives a plane wave from said direction of an antenna main beam. 
     
     
       13. The antenna system of claim 9 wherein said shaped main reflector and said shaped subreflectors are positioned and located near to references surfaces; the shaped main reflector having its central portion tangent to a reference surface paraboloidal in form and said subreflectors having central portions tangent to reference surfaces ellipsoidal or hyperboloidal in form, said reference subreflector surfaces being constructed and illuminated by radiators such that the angle β measured between the axis of the reference ellipsoid or the reference hyperboloid and the axis of the reference paraboloid satisfy the equation: ##EQU43## where Y c  is the middle point of the reference paraboloidal surface and where e is the eccentricity of the reference ellipsoidal or hydroboloidal subreflector surface and f is the focal length of the reference paraboloidal surface, and the angle α is measured between the axis of the horn radiator and the axis of the ellipsoid or hyperboloid can be found from the equation: ##EQU44## such that antenna patterns produced by an antenna composed of the reference paraboloidal reflector illuminated by an antenna feed consisting of a reference ellipsoidal or hyperboloidal subreflector and a radiator, whose phase center is located at one foci of the subreflector while the focal point of the reference paraboloidal reflector is located at the other subreflector foci, have circularly symmetric main beams and low cross polarization. 
     
     
       14. The antenna systems of claims 1 and 9 wherein the reflecting surface of said shaped main reflector is so shaped and constructed such that a family of rays, r 2 , reflected from one of said subreflectors are then incident upon the shaped main reflector and when reflected from the main shaped reflector surface produce another family of rays, r 3 , which rays are directed approximately parallel to the axis of said reference paraboloidal reflector surface which direction being also in the direction of the main beam of the radiation pattern produced by said radiator illuminating said subreflector which in turn illuminates said shaped main reflector; and said shaped main reflector surface being constructed as determined by ray interpolation among the incident family of rays, r 2 , at or near a point of incidence on said main reflector surface and by spatial extrapolation from said point using small spatial increments obtained from normal vectors to the said shaped main reflector surface, calculated from Snell's Law of reflection applied to rays obtained by said interpolation of rays, r 2 , said small spatial increments being connected successively to form reflector contours of the shaped main reflector surface from which contours the entire shaped main reflector surface can be constructed which directs said family of rays, r 3 , along the direction of said main beam of said radiation pattern which radiation pattern has sidelobes everywhere lower than 17 dB below main beam due to the elimination of aperture phase errors over said shaped main reflector aperture through said shaped construction of the main reflector.   
     
     
       15. The antenna systems of claims 1 and 9 wherein one of the shaped subreflectors is illuminated by two or more radiators to produce two or more independent antenna patterns with main beams in two or more given directions and with secondary pattern maxima below 15 dB; and wherein the forms of the caustic focal fields in one of the focal regions of the shaped subreflector when illuminated by each of the several horns are of similar form and position to the caustic fields in the region of the caustic fields of said shaped main reflector when the shaped main reflector receives plane waves from said given directions.   
     
     
       16. The antenna systems of claims 1 and 9 wherein the aperture illumination distribution is given by f(x,y), where f(x,y) denotes power per unit area, over the aperture of the shaped main reflector with center at x=0 and y=0 the edge contour of the shaped main reflector aperture being approximately circular in form; and one of said shaped subreflectors is constructed such that all ray paths, r 1 , from the center of phase of a radiator illuminating said shaped subreflector forming a family of rays, r 1 , which upon being reflected from the shaped subreflector form a family of rays, r 2 , which are focused to variable focal points or small focal regions F Q  and from thence forming a family of rays ρ which proceed from said variable focal points or small focal regions F Q  to the main shaped reflector surface where the family of rays ρ are reflected again producing the antenna pattern; and   wherein all ray path lengths, r 1 , r 2 , and ρ, obey the equation ##EQU45##   in which k o  is a constant and G(θ o , φ o ) describes the radiation pattern of said radiator, such that when f(x,y) describes an aperture power distribution over the antenna aperture which have very low power density along and near the edge of the antenna aperture said antenna systems produce an antenna pattern with sidelobe levels everywhere below a level of 30 dB referred to the peak of the antenna main beam.   
     
     
       17. The antenna system of claim 9 wherein said radiation patterns and their main beams are scanned in angular position by motions of the antenna feed or feeds including motions of separate portions of said feed or feeds while keeping the shaped main reflector in a fixed position. 
     
     
       18. The antenna system of claim 9 wherein said antenna patterns and their main beams are scanned in angular position by motions of the entire antenna system including the shaped main reflector while maintaining the antenna feed or feeds in a fixed position with respect to the shaped main reflector. 
     
     
       19. The antenna system of claim 9 wherein said antenna patterns and their main beams are scanned in angular positions by motions of the antenna feeds including the radiators and shaped subreflectors with respect to the location and position of the shaped main reflector which is also moved. 
     
     
       20. The antenna system of claim 9 wherein one of the radiation patterns produced by said antenna system has an antenna gain corresponding to an antenna aperture efficiency of greater than 80% and all secondary maxima are at least 17 dB below the level of the peak of the antenna main beam. 
     
     
       21. The antenna systems of claims 1 and 9 wherein one of said radiators being in the form of an electromagnetic horn is not attached to said shaped subreflector which it illuminates but is constructed by extending its impedance surfaces continuously such that the mouth of the horn radiator nearly touches the shaped subreflector near portions of the edge of said shaped subreflector in order that very little electromagnetic power is lost due to spillover around the edges of the shaped subreflector and allowing very little electromagnetic power to be blocked when passing from the shaped subreflector to the shaped main reflector while, at the same time, providing sufficient space between the horn radiator and the shaped subreflector for these portions of the antenna feed to be independently moved as required for scanning the main beam of antenna pattern produced by the antenna feed.